Write the cartesian equation of the following line given in vector form : ` vec r=2 hat i+ hat j-4 hat k+lambda\ ( hat i- hat j- hat k)`

Find the vector equation of the following planes in non parametric form: -> r=(2 hat i+2 hat j- hat k)+lambda( hat i+2 hat j+3 hat k)+mu(5 hat i-2 hat j+7 hat k)dot

Find the vector equation of the following planes in Cartesian form: vec r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i-2hat j+3hat k)

Find the vector equation of the following planes in scalar product form ( vec rdot vec n=d): vec r=( hat i+ hat j)+lambda( hat i+2 hat j- hat k)+mu(- hat i+ hat j-2 hat k)

Find the Cartesian form of the equation of the following plane: vec r=( hat i- hat j)+s(- hat i+ hat j+2 hat k)+t( hat i+2 hat j+ hat k)dot

Find the vector equation of the following plane in scalar product form vec r=(hat i-hat j)+lambda(hat i+2hat j-hat k)+mu(-hat i+hat j-2hat k)

Find angle between the vectors vec a=hat i+hat j-hat k and vec b=hat i-hat j+hat k

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

A point on the line vec r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

Find the angel between the vectors vec a=hat i-hat j+hat k and vec b=hat i+hat j-hat k

Find the vector and cartesian equation of a plane containing the two lines vec r=(2hat i+hat j-3hat k)+lambda(hat i+2hat j+5hat k) and vec r=(3hat i+3hat j+2hat k)+mu(3hat i-2hat j+5hat k) Also,show that the line vec r=(2hat i+5hat j+2hat k)+P(3hat i-2hat j+5hat k) lies in the plane.